leftnorm() [1/2]

SRDef syten::MPS::State::leftnorm	(	Index const	site,
		Truncation	trunc = Truncation(),
		State::DropNorm const	dropN = DropNorm::Yes,
		State::DropUnmatched const	dropU = DropUnmatched::lr
	)

Left-normalises the tensor \(X_i\) on the specified site as \(X_i^{\sigma_i} \to U^\sigma S V\) and multiplies the corresponding transformation \(SV\) in the next tensor on the right \(X_{i+1} \to SV X_{i+1}\).

After normalisation, the contraction of \(X\) with its hermitian conjugate over the physical and left indices should give an identity matrix:

.-→[+]--→     .--→
|   ↓      =  |
'-←[ ]--←     '--←

Parameters

site	location of tensor to normalise
trunc	Truncation specification
dropN	if tensors on all sites but site are normalised on entry, ensure that the state is normalised on exit.
dropU	whether, and if so, compared to where, drop unmatched blocks

Returns

the error incurred during truncation, calculated as \( sqrt(2 - 2 \sqrt(1-D)) \) where \( D \) is the squared sum of discarded singular values (see thesis for details) or -1 if no states have been kept.

If trunc is a default syten::Truncation object, a QR decomposition rather than a SVD is used.

References syten::clear(), dropUnmatched(), lInt, syten::MPS::norm(), syten::QR::qr(), rIdx, rInt, syten::singValSqdToError(), size(), syten::Tensor< rank >::size(), syten::SVD::svd(), SYTEN_ZNORM_THRESHOLD, uInt, and syten::underThreshold().

Referenced by syten::allSiteEntropy(), syten::mutualInfo::allSiteEntropy(), syten::MPS::apply_op_orthogonalise_fit(), syten::MPS::ProjectedPurification::correlator(), syten::mutualInfo::entropyOneSite(), syten::entropyOneSite(), syten::entropyTwoSite(), syten::mutualInfo::entropyTwoSite(), syten::Pyten::init_mps(), leftnorm(), syten::MPS::ProjectedPurification::local_expectation(), syten::MPS::Snapshots::Workspace::move_to_site(), syten::MPS::RDMs::OrbRDM::OrbRDM(), syten::MPS::orthogonalise_variational(), syten::MPS::TDVP::Worker::sync(), truncate(), truncateVariational(), syten::MPS::DMRG::Worker::Worker(), and syten::MPS::TDVP::Worker::Worker().

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